Check your math addition - casting out nines trick - By tecmath
Transcript
| 00:0-1 | you know , welcome to the Tech Math channel . | |
| 00:01 | What we're going to be having a look at in | |
| 00:02 | this video is how to check your answers in maths | |
| 00:05 | and to check your addition answers . In this particular | |
| 00:08 | video , you're making a whole bunch of videos , | |
| 00:10 | looking at checking your addition , your subtractions , your | |
| 00:13 | divisions and you're more applications and how to make sure | |
| 00:16 | you're going to get these right Now . The method | |
| 00:18 | for our , I'd be using for working out whether | |
| 00:21 | or not my addition answers were correct . Was this | |
| 00:24 | method through casting out nines . So I'm gonna show | |
| 00:26 | you how this works . So say we added the | |
| 00:29 | following numbers 3070 for we add 6,017 , We add | |
| 00:36 | 13,000 814 , we add 1810 , we had 27 | |
| 00:45 | to this . And then while we're at it we | |
| 00:46 | think let's add 3,611 . So we add all this | |
| 00:50 | together and being utter genius is instantly we come up | |
| 00:53 | with the answer of 28,353 . So how can we | |
| 00:59 | check to see that indeed are geniuses correct ? And | |
| 01:03 | that we are right on the right track . So | |
| 01:06 | we use this method called Carson at the nines and | |
| 01:08 | this is a really really simple method , we do | |
| 01:12 | it as follows . First off we're gonna be looking | |
| 01:14 | at each one of these numbers here , we're gonna | |
| 01:16 | be adding the digits of the numbers but anyway we | |
| 01:19 | see at nine we can get rid of those . | |
| 01:21 | So I'll show you I mean here we're gonna be | |
| 01:23 | adding three and seven and four . None of those | |
| 01:26 | digits together add up to nine . So we're gonna | |
| 01:28 | be adding three and 74 so we do that we | |
| 01:30 | get the answer of 14 but with casting out nines | |
| 01:33 | , what we're actually after is we're after reducing it | |
| 01:35 | to a single digit number . So once again we | |
| 01:38 | do the same thing we do with the one and | |
| 01:39 | four , we add these together we get five . | |
| 01:43 | Okay , go the next number there . Six and | |
| 01:45 | one is seven plus seven is 14 and one in | |
| 01:50 | four is five . Okay because there's no one there | |
| 01:53 | , we can throw it any night but on 13,804 | |
| 01:56 | and if you look at this 13814 one and eight | |
| 02:01 | here add up to nine . We can cast in | |
| 02:03 | a way we can throw it away . So we're | |
| 02:04 | left with just adding 31 and four which add up | |
| 02:08 | to eight In 1810 . The one of the eight | |
| 02:13 | up tonight , we can get rid of them and | |
| 02:14 | cast them away . We're left with just the one | |
| 02:17 | , two and 7 . These add up to nine | |
| 02:19 | . We can cast a whole lot of way . | |
| 02:21 | 3611 3 . And the six had up to nine | |
| 02:25 | so we're left with just one and one which equals | |
| 02:28 | two . So as far as the things we're adding | |
| 02:33 | , This is what we're left with so far we | |
| 02:35 | can again cast out 90 and we're gonna add our | |
| 02:38 | digits here . Cast away the nines and then add | |
| 02:41 | what we have left . five and 5 is 10 | |
| 02:44 | plus two is 12 , reduce this even further And | |
| 02:48 | we're left with a three . Okay . one plus | |
| 02:51 | 2 is three . Okay I didn't take that long | |
| 02:54 | . And so now what we're gonna do is we're | |
| 02:56 | gonna do the same for answers here . Is there | |
| 02:59 | any uh Any that add up to nine in here | |
| 03:02 | that you can see ? No there's not unfortunately nothing | |
| 03:05 | that easy . So two and 8 is a 10 | |
| 03:11 | 13 18 21 Just adding as I go along and | |
| 03:16 | two or one we reduce this is three . So | |
| 03:19 | what you notice is these two numbers match . And | |
| 03:22 | if that's the case of these two numbers match , | |
| 03:24 | you can assume your answer is correct . Okay . | |
| 03:27 | No this method is not 100% proof . Okay , | |
| 03:30 | it's not 100% proof of the correct answer because maybe | |
| 03:33 | our digits here would be in a different order so | |
| 03:35 | we could actually get a three here and it wouldn't | |
| 03:38 | be 100% necessarily correct . But what it does do | |
| 03:42 | is there are answers don't match . It shows that | |
| 03:44 | we actually definitely have an error . Okay so let's | |
| 03:47 | have a look at another example of this . I'll | |
| 03:50 | get you to do this example . Okay ? Um | |
| 03:54 | and then practice a few on your own . Okay | |
| 03:56 | so let's go to this one here . What about | |
| 03:59 | 6,132 . 1,874 , 20 . 1000 110 27 . | |
| 04:15 | 305 60241 . And we add all these together and | |
| 04:25 | We get I'm gonna run our room . I reckon | |
| 04:27 | that's what we're going to get is 109 . What | |
| 04:30 | is that ? We get Uh get rid of that | |
| 04:35 | . That's what we do . We get 109,290 is | |
| 04:43 | our total ? Okay ? I'll try to fit a | |
| 04:45 | line under that . We did pretty well , didn't | |
| 04:47 | we ? Okay so now we're gonna use casting out | |
| 04:50 | nines to check our answers . It's all the time | |
| 04:53 | . We look at 6132 . These two numbers that | |
| 04:57 | up tonight we can get rid of them were left | |
| 04:58 | with one plus two equals three . You do the | |
| 05:00 | rest Okay ? So hopefully a pause and down the | |
| 05:05 | rest one and 8 is nine . So we're left | |
| 05:08 | with seven and 4 which is 11 and one and | |
| 05:11 | 1 out of 11 is too okay Get rid of | |
| 05:16 | the nine . Then we live with 16 and one | |
| 05:19 | . These add up to eight two plus one plus | |
| 05:22 | one plus one is five , two and 7 and | |
| 05:25 | up to nine . Get rid of them three and | |
| 05:28 | 58 And six and 2 and a four and a | |
| 05:32 | one . We can actually get rid of the 6th | |
| 05:35 | or two And the one because they had up to | |
| 05:37 | nine and we're left with a four . Once again | |
| 05:41 | we can start casting out things here casting at nine | |
| 05:44 | so we can get rid of that and we're left | |
| 05:46 | with a three or two and ate and ate . | |
| 05:48 | You might be able to look at that and say | |
| 05:50 | look two and 8 and I actually add up to | |
| 05:55 | 18 which nine goes into . You can actually get | |
| 05:58 | rid of those to any number that night goes into | |
| 05:59 | . Brother was going to add them normally 32 is | |
| 06:01 | five , five is 13 and 21 . Okay 21 | |
| 06:11 | : one . We should be putting in here three | |
| 06:15 | , shouldn't we ? Because I have to reduce it | |
| 06:17 | so we can cast that nines down here And we | |
| 06:20 | live with one and 2 which is three our answers | |
| 06:24 | match . We've got a pretty good likelihood that our | |
| 06:26 | answer here is correct . Okay So anyway that's the | |
| 06:30 | way you use casting out nines to check your addition | |
| 06:33 | answers . It's a really really great method . Once | |
| 06:36 | again it does not give 100% proof but it gives | |
| 06:39 | a fairly fairly good uh , you know , likelihood | |
| 06:43 | that it's a correct answer anyway . Hopefully that was | |
| 06:45 | just some help . I'm gonna be making a video | |
| 06:47 | next . Let's be looking at the best methods of | |
| 06:50 | subtraction checking . Okay , bye . |
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Check your math addition - casting out nines trick is a free educational video by tecmath.
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